That's not the negation. It's logically equivalent. If P is false, then saying "If P then Q" has no useful information. To say "If it is raining then you will get wet" doesn't tell you anything about whether you will get wet if it's not raining.

No! The implication is "P implies Q". NOT "not P implies Q". "If it IS raining, you will get wet." And WHAT is supposed to be true?? Any of these statements can by either true or false. What you are trying to show is that two of them are logically equivalent. Those two are not.

Inclusive or means A is true OR B is true OR both are true. As long as any one of those is true, the statement is true.

Assuming the statement "if it is raining then you will get wet" is true, it certainly also true that "either it is not raining or you will get wet" is true. It happens that here they can't BOTH be true but they don't have to: only one of them has to be true.